Exponential moments of affine processes

TL;DR

This paper characterizes the domain of the moment generating function for affine processes, extending previous results to more general jump behaviors and state spaces, and confirms the affine transform formula's validity.

Contribution

It generalizes the understanding of exponential moments for affine processes, allowing for broader jump behaviors and state spaces, with both necessary and sufficient conditions for moment finiteness.

Findings

Extended the domain of exponential moments for affine processes.

Validated the affine transform formula under broader conditions.

Provided necessary and sufficient conditions for exponential moment finiteness.

Abstract

We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovi\'{c} and Schachermayer [Ann. Appl. Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovi\'{c} and Mayerhofer [Radon Ser. Comput. Appl. Math. 8 (2009) 1-40] and Kallsen and Muhle-Karbe [Stochastic Process Appl. 120 (2010) 163-181]) in that it allows processes with very general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.